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You shouldn't attempt to build an inverter without a transformer. If not anything else, it'll at least provide isolation.
What I think you want is a design without using bulky iron/steel core transformer.
What you need is not a transformerless inverter, but an SMPS inverter.
You can find a basic block diagram here:
The first stage is something like this:
You need to use a ferrite transformer. A ferrite transformer is very small but can handle a lot of power, but should be operated at much higher frequency. So, first you need to step up 12V to about 300VDC using high-frequency. And then you need to convert that 300VDC again to 220VAC, using a full-bridge converter.
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